WASHINGTON, Dec 4 (Reuters) - U.S. congressional Republicans had wanted to show a united front against President Barack Obama’s demand for tax hikes, but their tenuous coalition showed signs of strain on Tuesday.

Just a day after House Speaker John Boehner unveiled a “fiscal cliff” counteroffer with some concessions on revenues, he faced a criticism from some conservatives and what appeared to be a wait-and-see approach from others.

As lawmakers voiced their opinions, Boehner presided over a purge of some Republicans regarded as party dissidents from plum House committee assignments. One of those ousted called the moves “petty” and “vindictive.”

The infighting threatened to undermine Republicans’ negotiating position as Congress and the White House try to avoid $600 billion worth of automatic tax hikes and spending cuts in the new year by reaching a landmark deal to shrink deficits.

The top U.S. Senate Republican offered only tepid support, stopping well short of endorsing Boehner’s offer to increase revenues by $800 billion by eliminating tax deductions and credits.

“I think it is important that the House Republican leadership has tried to move the process forward,” Senate Republican leader Mitch McConnell told reporters.

Many Republicans, especially the most conservative, see the offer as the very tax hike they pledged to avoid, even though it would not increase rates.

Obama stood firm on his demand that tax rates on the wealthiest must rise as part of a deal to avert the fiscal cliff.

CONSERVATIVES HOWL

Senator Jim DeMint, of South Carolina, a favorite of the anti-tax Tea Party movement, said the plan would “destroy jobs” and let Washington continue to grow U.S. deficits.

DeMint’s comments, along with criticism from other conservative lawmakers, showed Boehner faces pressure to stand firm against raising taxes while some in his ranks believe he needs to do so to obtain the elusive common ground with Obama’s Democrats.

“This isn’t rocket science. Everyone knows that when you take money out of the economy (with tax hikes), it destroys jobs, and everyone knows that when you give politicians more money, they spend it,” DeMint said.

“This is why Republicans must oppose tax increases and insist on real spending reductions that shrink the size of government and allow Americans to keep more of their hard-earned money,” the South Carolina Republican said.

Republican Representative Tom Cole of Oklahoma - who last week suggested Republicans cave to Obama’s demands to renew tax cuts for income of up to $250,000 while allowing those on higher income to expire next month - voiced support for Boehner.

“There is a difference between suggesting a play to the quarterback and tackling him when he runs something else,” Cole said.

“I recognize that the speaker makes the final call and he has my complete support,” Cole said, predicting Boehner will reach a bipartisan deal that’s backed by most House Republicans.

“I sense cautious optimism,” Cole said.

As for DeMint’s comments, Cole said, “I have a lot of respect for Jim DeMint. But criticism has to be coupled with something that is political possible to be useful,” Cole said.

The internal Republican disputes are a sign of frustration that Obama and his Democrats appear to have the upper hand, said Greg Valliere of the Potomac Research Group, which tracks Washington politics for institutional investors. All Obama needs to do is wait and taxes will rise, although that risks damaging the economy.

“Republicans realize they will get much of the blame if we go over the cliff. And as they game out the ultimate outcome - which inevitably will include major compromises - they are acting more frustrated in public,” Valliere said.

COMMITTEE PURGE

Two of the most conservative House members also lashed out at Boehner’s leadership after he led an effort to remove them from plum assignments on the House Budget Committee.

Representatives Tim Huelskamp of Kansas and Justin Amash of Michigan - both Tea Party favorites - said they were purged from the panel because they defied leadership too often to defend their conservative principles. Two other Republicans also lost assignments on other committees.

Both Amash and Huelskamp voted against last year’s deal to raise the debt limit and cast the only Republican votes in the House Budget Committee against the budget plan this year authored by panel chairman Paul Ryan.

Huelskamp called his ouster “petty” and “vindictive.”

“What this says is that dissent will not be tolerated, particularly conservative dissent,” he told an audience at the conservative Heritage Foundation think tank.

He added that Boehner wanted to silence opposition to a deal that would raise taxes.

“I think this makes it very clear to conservatives that you’re about to get run over. Sit down and just lump it,” he said.

A senior House Republican aide said Boehner was not upset by pot shots from some within the party’s ranks.

“DeMint is a member of the far right,” the senior aide said. “You would prefer that he bite his lip and not offer his criticism. But I don’t think it is going to have any impact on the dynamics.”

Boehner anticipates that dozens in his party will vote against any deal, but still believes he can win a majority -- perhaps two-thirds -- of House Republicans, the aide said.